In the context of partial actions of Hopf algebras, it is proved that a partial action of a
Hopf algebra on a unital algebra \(A\)  admits an enveloping action \((B, \theta )\)  if and only if each of
the ideals \(\theta (A)\unrhd B\)  is a unital algebra in [1]}.
In this section, we mainly extend this famous result to partial twisted smash products.
